What is the ruling on a couple returning to each other after the third divorce without a حلل (muḥallil), if they regret it and wish to reconcile?

It is the Muslim's duty to govern by the Sharia (definition) of Allah and to submit to it. Allah knows best the harm that divorce entails. If a man divorces his wife three times with a single utterance, she becomes unlawful for him until she marries another husband, according to the majority of scholars. If she is divorced three times with multiple utterances, after a رجعة (reconciliation) each time, she does not become lawful for him until she marries another husband, based on the Almighty's saying: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband." It is not permissible for a man to marry with the intention of making the woman lawful for her previous husband (حل الـتيس المستعار - temporary marriage of convenience), for the Prophet, peace and blessings be upon him, cursed the one who makes a woman lawful for her previous husband and the one for whom she is made lawful.